University of Zagreb (p.p. 407 Trg maršala Tita 14 HR-10002 ZAGREB, CROATIA Phone: (+385 1) 4564 111 Fax: (+ 385 1) 4830 602 - Croatie)
Abstract : Dulac series are asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras of power-log transseries (generalized series) which extend the algebra of Dulac series. We give a formal normal form and prove a formal embedding theorem for transseries in these algebras.
Pavao Mardešić, Maja Resman, Jean-Philippe Rolin, Vesna Županović. Normal forms and embeddings for power-log transseries. Advances in Mathematics, Elsevier, 2016, 303, pp.888 - 953. ⟨10.1016/j.aim.2016.08.030⟩. ⟨hal-01414966⟩